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Chapter 12: Q. 1 (page 987)

Give precise mathematical definitions or descriptions of each of the following concepts that follow. Then illustrate the definition with a graph or an algebraic example.

* a level curve for f (x, y)

Short Answer

Expert verified

A level curve of a function f(x, y) is the curve of points (x, y) where f(x, y) is some constant value.

Step by step solution

01

Step 1. Given Information.

A level curve for f(x, y).

02

Step 2. Definition.

A level curve of a function f(x, y) is the curve of points (x, y) where f(x, y) is some constant value. A level curve is simply a cross section of the graph of z=f(x,y)taken at a constant value, sayz=c. A function has many level curves, as one obtains a different level curve for each value of c in the range of f(x, y).

03

Step 3. Example.

Forthefunctionf(x,y)=-x2-2y2.Thelevelcurvesarec=-1,-2,-3,....,-10.

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